{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "google",
   "metadata": {},
   "source": [
    "##### Copyright 2023 Google LLC."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "apache",
   "metadata": {},
   "source": [
    "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "you may not use this file except in compliance with the License.\n",
    "You may obtain a copy of the License at\n",
    "\n",
    "    http://www.apache.org/licenses/LICENSE-2.0\n",
    "\n",
    "Unless required by applicable law or agreed to in writing, software\n",
    "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "See the License for the specific language governing permissions and\n",
    "limitations under the License.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "basename",
   "metadata": {},
   "source": [
    "# wedding_optimal_chart"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "link",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "<td>\n",
    "<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/contrib/wedding_optimal_chart.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
    "</td>\n",
    "<td>\n",
    "<a href=\"https://github.com/google/or-tools/blob/main/examples/contrib/wedding_optimal_chart.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
    "</td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "doc",
   "metadata": {},
   "source": [
    "First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "install",
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install ortools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "code",
   "metadata": {},
   "outputs": [],
   "source": [
    "#\n",
    "# Copyright 2018 Turadg Aleahmad\n",
    "#\n",
    "# Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "# you may not use this file except in compliance with the License.\n",
    "# You may obtain a copy of the License at\n",
    "#\n",
    "#     http://www.apache.org/licenses/LICENSE-2.0\n",
    "#\n",
    "# Unless required by applicable law or agreed to in writing, software\n",
    "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "# See the License for the specific language governing permissions and\n",
    "# limitations under the License.\n",
    "\n",
    "from ortools.constraint_solver import pywrapcp\n",
    "from ortools.constraint_solver import solver_parameters_pb2\n",
    "\"\"\"Finding an optimal wedding seating chart.\n",
    "\n",
    "From\n",
    "Meghan L. Bellows and J. D. Luc Peterson\n",
    "\"Finding an optimal seating chart for a wedding\"\n",
    "http://www.improbable.com/news/2012/Optimal-seating-chart.pdf\n",
    "http://www.improbable.com/2012/02/12/finding-an-optimal-seating-chart-for-a-wedding\n",
    "\n",
    "Every year, millions of brides (not to mention their mothers, future\n",
    "mothers-in-law, and occasionally grooms) struggle with one of the\n",
    "most daunting tasks during the wedding-planning process: the\n",
    "seating chart. The guest responses are in, banquet hall is booked,\n",
    "menu choices have been made. You think the hard parts are over,\n",
    "but you have yet to embark upon the biggest headache of them all.\n",
    "In order to make this process easier, we present a mathematical\n",
    "formulation that models the seating chart problem. This model can\n",
    "be solved to find the optimal arrangement of guests at tables.\n",
    "At the very least, it can provide a starting point and hopefully\n",
    "minimize stress and arguments.\n",
    "\n",
    "Adapted from\n",
    "https://github.com/google/or-tools/blob/main/examples/csharp/wedding_optimal_chart.cs\n",
    "\"\"\"\n",
    "\n",
    "\n",
    "def main():\n",
    "  # Instantiate a CP solver.\n",
    "  parameters = pywrapcp.Solver.DefaultSolverParameters()\n",
    "  solver = pywrapcp.Solver(\"WeddingOptimalChart\", parameters)\n",
    "\n",
    "  #\n",
    "  # Data\n",
    "  #\n",
    "\n",
    "  # Easy problem (from the paper)\n",
    "  # n = 2  # number of tables\n",
    "  # a = 10 # maximum number of guests a table can seat\n",
    "  # b = 1  # minimum number of people each guest knows at their table\n",
    "\n",
    "  # Slightly harder problem (also from the paper)\n",
    "  n = 5  # number of tables\n",
    "  a = 4  # maximum number of guests a table can seat\n",
    "  b = 1  # minimum number of people each guest knows at their table\n",
    "\n",
    "  # Connection matrix: who knows who, and how strong\n",
    "  # is the relation\n",
    "  C = [[1, 50, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "       [50, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "       [1, 1, 1, 50, 1, 1, 1, 1, 10, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "       [1, 1, 50, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "       [1, 1, 1, 1, 1, 50, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "       [1, 1, 1, 1, 50, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "       [1, 1, 1, 1, 1, 1, 1, 50, 1, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "       [1, 1, 1, 1, 1, 1, 50, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "       [1, 1, 10, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "       [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 50, 1, 1, 1, 1, 1, 1],\n",
    "       [0, 0, 0, 0, 0, 0, 0, 0, 0, 50, 1, 1, 1, 1, 1, 1, 1],\n",
    "       [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n",
    "       [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n",
    "       [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n",
    "       [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n",
    "       [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n",
    "       [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]]\n",
    "\n",
    "  # Names of the guests. B: Bride side, G: Groom side\n",
    "  names = [\n",
    "      \"Deb (B)\", \"John (B)\", \"Martha (B)\", \"Travis (B)\", \"Allan (B)\",\n",
    "      \"Lois (B)\", \"Jayne (B)\", \"Brad (B)\", \"Abby (B)\", \"Mary Helen (G)\",\n",
    "      \"Lee (G)\", \"Annika (G)\", \"Carl (G)\", \"Colin (G)\", \"Shirley (G)\",\n",
    "      \"DeAnn (G)\", \"Lori (G)\"\n",
    "  ]\n",
    "\n",
    "  m = len(C)\n",
    "\n",
    "  NRANGE = range(n)\n",
    "  MRANGE = range(m)\n",
    "\n",
    "  #\n",
    "  # Decision variables\n",
    "  #\n",
    "  tables = [solver.IntVar(0, n - 1, \"x[%i]\" % i) for i in MRANGE]\n",
    "\n",
    "  z = solver.Sum([\n",
    "      C[j][k] * (tables[j] == tables[k])\n",
    "      for j in MRANGE\n",
    "      for k in MRANGE\n",
    "      if j < k\n",
    "  ])\n",
    "\n",
    "  #\n",
    "  # Constraints\n",
    "  #\n",
    "  for i in NRANGE:\n",
    "    minGuests = [(tables[j] == i) * (tables[k] == i)\n",
    "                 for j in MRANGE\n",
    "                 for k in MRANGE\n",
    "                 if j < k and C[j][k] > 0]\n",
    "    solver.Add(solver.Sum(minGuests) >= b)\n",
    "\n",
    "    maxGuests = [tables[j] == i for j in MRANGE]\n",
    "    solver.Add(solver.Sum(maxGuests) <= a)\n",
    "\n",
    "  # Symmetry breaking\n",
    "  solver.Add(tables[0] == 0)\n",
    "\n",
    "  #\n",
    "  # Objective\n",
    "  #\n",
    "  objective = solver.Maximize(z, 1)\n",
    "\n",
    "  #\n",
    "  # Search\n",
    "  #\n",
    "  db = solver.Phase(tables, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT)\n",
    "\n",
    "  solver.NewSearch(db, [objective])\n",
    "\n",
    "  while solver.NextSolution():\n",
    "    print(\"z:\", z)\n",
    "    print(\"Table: \")\n",
    "    for j in MRANGE:\n",
    "      print(tables[j].Value(), \" \")\n",
    "    print()\n",
    "\n",
    "    for i in NRANGE:\n",
    "      print(\"Table %d: \" % i)\n",
    "      for j in MRANGE:\n",
    "        if tables[j].Value() == i:\n",
    "          print(names[j] + \" \")\n",
    "      print()\n",
    "\n",
    "    print()\n",
    "\n",
    "  solver.EndSearch()\n",
    "\n",
    "  print()\n",
    "  print(\"Solutions: %d\" % solver.Solutions())\n",
    "  print(\"WallTime: %dms\" % solver.WallTime())\n",
    "  print(\"Failures: %d\" % solver.Failures())\n",
    "  print(\"Branches: %d\" % solver.Branches())\n",
    "\n",
    "\n",
    "main()\n",
    "\n"
   ]
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 5
}
